The weakly-compressible smoothed particle hydrodynamics (WCSPH) models offer distinct advantages in simulating free-surface flow. Within the rapidly evolving WCSPH field, Classical WCSPH model, based on the artificial viscous term, and its derived models, which additionally introduce numerical diffusive terms into the continuity equations - including the -SPH, -SPH, -SPH, --SPH, and -SPH models have gained prominence recently. The numerical diffusive term is found to alter the particle distributions in the free-surface region, leading to a change in the mean water level that reflects the volume conservation, which might result in inaccuracies in some simulations. This study evaluates the volume conservations of the aforementioned WCSPH models for flows at quasi-hydrostatic states evolved from varying levels of flow violence under prolonged simulations, through a series of numerical tests involving hydrostatic, standing-wave, and dam-break cases. For the hydrostatic and standing-wave cases, the performance of different types of WCSPH models remains consistent overall. The Classical WCSPH and --SPH models exhibit minimal changes in volume, with almost no decrease in the mean water level occurring. The -SPH, -SPH, -SPH models demonstrate decreases in the mean water level converging to around 0.2 times the SPH particle diameter (Δx), indicating favorable volume conservation. Conversely, the -SPH model consistently exhibits a decrease in the mean water level exceeding 1 Δ at = 2000s in a linear fashion, resulting in a noticeable reduction in volume. Under the dam-break case, most of the mean water levels simulated by different models experience a small increase, which is close to the decrease observed under the hydrostatic and standing-wave cases with corresponding models. Only the -SPH model continues to show a continuous decreasing tendency. In summary, considering volume conservation, the --SPH model demonstrates the best performance (excluding the Classical WCSPH model as it cannot simulate violent flow), followed by the -SPH, -SPH, -SPH and -SPH models.

中文翻译：

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不同暴力程度流量的SPH模型体积守恒比较研究

弱可压缩平滑粒子流体动力学 (WCSPH) 模型在模拟自由表面流方面具有明显的优势。在快速发展的 WCSPH 领域中，基于人工粘性项的经典 WCSPH 模型及其派生模型，在连续性方程中额外引入了数值扩散项 - 包括 -SPH、-SPH、-SPH、--SPH 和-SPH 模型最近受到关注。研究发现数值扩散项会改变自由表面区域的颗粒分布，导致反映体积守恒的平均水位发生变化，这可能会导致某些模拟不准确。本研究通过一系列涉及静水、驻波和溃坝情况的数值测试，评估了上述 WCSPH 模型在长时间模拟下从不同水平的流动暴力演变而来的准静水状态下的体积守恒。对于静水和驻波情况，不同类型的 WCSPH 模型的性能总体保持一致。经典的 WCSPH 和 --SPH 模型的体积变化很小，平均水位几乎没有下降。 -SPH、-SPH、-SPH 模型表明平均水位下降，收敛到 SPH 颗粒直径 (Δx) 的 0.2 倍左右，表明有利的体积守恒。相反，-SPH 模型始终表现出平均水位在 = 2000 秒时以线性方式下降超过 1 Δ，导致体积明显减少。溃坝工况下，不同模型模拟的平均水位大多出现小幅上升，与相应模型静水工况和驻波工况下观测到的下降量接近。只有-SPH模型继续呈现出持续下降的趋势。综上所述，考虑到体积守恒，--SPH模型表现出最好的性能（不包括经典的WCSPH模型，因为它不能模拟暴力流），其次是-SPH、-SPH、-SPH和-SPH模型。